- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Find the ratio in which the line $ 2 x+3 y-5=0 $ divides the line segment joining the points $ (8,-9) $ and $ (2,1) $. Also find the coordinates of the point of division.

Given:

The line \( 2 x+3 y-5=0 \) divides the line segment joining the points \( (8,-9) \) and \( (2,1) \).

To do:

We have to find the ratio in which the line \( 2 x+3 y-5=0 \) divides the line segment joining the points \( (8,-9) \) and \( (2,1) \) and the coordinates of the point of division.

Solution:

Let the line $2 x+3 y-5=0$ divides the line segment joining the points $A(8,-9)$ and $B(2,1)$ in the ratio $k: 1$ at point $P$.

Using section formula, we get,

$(x,y)=(\frac{mx_{2}+nx_{1}}{m+n}, \frac{my_{2}ny_{1}}{m+n})$

Coordinates of $P=(\frac{k(2)+1(8)}{2+1}, \frac{k(1)+1(-9)}{2+1})$

$=(\frac{2k+8}{k+1}, \frac{k-9}{k+1})$

Point $P$ lies on the line $2 x+3y-5=0$.

This implies,

$2(\frac{2k+8}{k+1})+3(\frac{k-9}{k+1})-5=0$

$2(2k+8)+3(k-9)-5(k+1)=0$

$4k+16+3k-27-5 k-5=0$

$2k-16=0$

$k=8$

$\Rightarrow k: 1=8: 1$

Therefore, the point $P$ divides the line in the ratio $8: 1$.

The point of division $P=(\frac{2(8)+8}{8+1}, \frac{8-9}{8+1})$

$=(\frac{16+8}{9},\frac{-1}{9})$

$=(\frac{24}{9}, \frac{-1}{9})$

$=(\frac{8}{3}, \frac{-1}{9})$

Hence, the required point of division is $(\frac{8}{3}, \frac{-1}{9})$.

- Related Articles
- Find the ratio in which the y-axis divides the line segment joining the points $(5, -6)$ and $(-1, -4)$. Also, find the coordinates of the point of division.
- Find the ratio in which the y-axis divides line segment joining the points $( -4,\ -6)$ and $( 10,\ 12)$. Also find the coordinates of the point of division.
- Determine the ratio in which the straight line $x – y – 2 = 0$ divides the line segment joining $(3, -1)$ and $(8, 9)$.
- Find the ratio in which point $P( x,\ 2)$ divides the line segment joining the points $A( 12,\ 5)$ and $B( 4,\ −3)$. Also find the value of $x$.
- Find the ratio in which the point $P (x, 2)$ divides the line segment joining the points $A (12, 5)$ and $B (4, -3)$. Also, find the value of $x$.
- In what ratio is the line segment joining the points $(-2, -3)$ and $(3, 7)$ divided by the y-axis? Also find the coordinates of the point of division.
- Find the ratio in which the points $(2, y)$ divides the line segment joining the points $A (-2, 2)$ and $B (3, 7)$. Also, find the value of $y$.
- Find the ratio in which the line segment joining the points $A (3, -3)$ and $B (-2, 7)$ is divided by x-axis. Also, find the coordinates of the point of division.
- Point $P( x,\ 4)$ lies on the line segment joining the points $A( -5,\ 8)$ and $B( 4,\ -10)$. Find the ratio in which point P divides the line segment AB. Also find the value of x.
- The mid-point $P$ of the line segment joining the points $A (-10, 4)$ and $B (-2, 0)$ lies on the line segment joining the points $C (-9, -4)$ and $D (-4, y)$. Find the ratio in which $P$ divides $CD$. Also, find the value of $y$.
- Show that the mid-point of the line segment joining the points $(5, 7)$ and $(3, 9)$ is also the mid-point of the line segment joining the points $(8, 6)$ and $(0, 10)$.
- Find the ratio in which the line segment joining $A(1, -5)$ and $B(-4, 5)$ is divided by the x-axis. Also, find the coordinates of the point of division.
- Find the coordinates of the point which divides the line segment joining $(-1, 3)$ and $(4, -7)$ internally in the ratio $3 : 4$.
- Find the point which divides the line segment joining the points $(7,\ –6)$ and $(3,\ 4)$ in ratio 1 : 2 internally.
- Determine the ratio, in which the line $2x + y - 4 = 0$ divides the line segment joining the points $A(2, -2)$ and $B(3, 7)$.